The following methods will help you to resolve your issue:
1. Transfer the PST file to OWA account via Drive Shipping method.
Follow the given steps to upload the file:
Copy the MS Outlook PST files to a BitLocker-encrypted hard disk.
Now, physically ship the hard drive to Microsoft.
Microsoft will upload the received Outlook PST database in the cloud of Microsoft.
You can use the Outlook 365 import service and migrate the PST to Exchange Online.
2. Export Outlook PST files to Office 365 account via Network Upload.
Follow these steps for this solution:
1. Copy SAS URL & install Azure AzCopy.
2. Transfer Outlook PST files to O365.
3. View the entire list of uploaded Outlook Data files.
4. Create PST Import Mapping file.
5. Create PST Import Job.
To know more about these solutions in detail, visit the following link: http://www.office365tips.org/import-outlook-pst-to-exchange-online/
Is there also a way to make the upload for the PST go faster? It seems like azcopy is only using 25% of my upload speed.